435 



This simplification agrees with equation (u) within 7» over the range z = 7.8, 

 C = 0.063 (l oz. at 6 feet depth) to z„ = 2, C = O.ll («75 lb. at 93 feet). 



Co'npari son wt t h a V '^ Law of Seal in 'j 



Let S be the abfolute displaceinent of the bubble at the end of the first period in any 

 particular set up of charge and surfaces. Let S be the bubble displacencnt in a geometrically 

 similar set up where all dimensions are increased in the ratio \, the charge weight being increased 

 in the ratio \. Then it follows at once from equation (12) that 



S^ = \* S (13) 



Equation (13) is independent of the depth e.t which the explosion occurs. If the 

 displacement had scaled according to the W I-) law s'- would have been equil toXS, so that (13) 

 indicates that the displacement of a lirge explosion bubble is less than the value obtained by 

 scaling up from a small scale experiment. 



Qir.clusion . 



The effect of surfaces on an explosion bubble has been shown to be due to two principal 

 causes, viz., the velocity imparted to the water near the bubble by the image sources, and the 

 pressure gradient set up in the water by the image sources. It Is found that to calculate the 

 effect it is necessary only to calculate the space gradient, along the axis of symmetry, of the 

 velocity pottntial due to the inHgt sources produced by a unit source at the explosion centre. 

 A simple formula, equations (ll) or (12), then enables the displacement of tne bubble in the first 



oscillation to be calculated. These displacsirents are almost independent of depth, A table of "t, 



values of the coefficient 2.^ In equations (ll) and (12) is appended for convenience. '^' 



' iC 



References . J J' 



X> * 



(1) Theory of the "ulsations of the Gas Bubble formed by an Underwater explosi.on. jkw' 

 Report No. C4-sr20-010. *"C 



'-% 



(2) The Motion and Shape of the Hollow Produced by an Explosion in a Liquid. 



G.I. Taylor and R.M. Davies. 



(3) cf. "The motion and shape of the hollow produced by an explosion in a liquid', 

 G.I. Taylor and R.M. Davies, where the bubble is represented by a point source 

 and a oipole and the effect of the images due to each Is considered, 



(4) This result is also given by Savic. 



(5) Calculated from Savic's equatitin for the potential due to the images by 

 d|ffer6nt iat ing with respect to d his expression for w. 



